Radar rainfall estimation technique when attenuation is negligible

ABSTRACT

A method of using a bipolar radar to estimate a precipitation rate for rain that generates negligible attenuation. The method includes using the bipolar radar to measure the differential phase Φ DP  and the apparent reflectivity Z e  on at least one of horizontal polarization H and vertical polarization V over a given interval [r 0 , r 1 ] of path radii relative to the radar. An estimate of the value N o * representative of the dimensional distribution of rain drops is made on the basis of the differential phase difference in the range r 0  to r 1  and on the basis of an integral of a function of the apparent reflectivity Z e  along the interval [r 0 , r 1 ]. A value is deduced for the precipitation rate at a point from N 0 * and the apparent reflectivity at the point.

This is a nationalization of PCT/FR02/02447 filed Jul. 11, 2002 andpublished in French.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to meteorological techniques forestimating a precipitation rate by means of radar.

2. Description of the Related Art

When estimating the rate of rainfall from radar measurements, one isgenerally confronted with the problem of attenuation of the radar wave,and with the problem of the natural variability of rain.

The concept of coherent radar with polarization diversity associatedwith a so-called ZPHI algorithm is described in WO 99/38028 as asolution for those two obstacles under operational conditions.

ZPHI is a profiler algorithm which basically uses as input a measuredreflectivity profile Z_(a) and a constraint given by a differentialphase difference Φ_(DP) between two points r₁ and r₂ on a line of sight.

On the basis of those measurements, the specific attenuation A and aparameter known as N₀* are determined, which parameter quantifies thedistribution of raindrop sizes.

The rainfall rate R to be estimated is obtained as a function of thosetwo parameters for two reasons. First, the specific attenuation A is notsubject to attenuation effects. Using it to estimate R thus enables theattenuation problem to be overcome. Second, the parameter N₀* sufficesto describe the natural variability of rain.

The ZPHI algorithm is equally applicable in the X and C bands, whichfrequency bands are sensitive to attenuation.

SUMMARY OF THE INVENTION

The present specification relates to a method extended from the ZPHImethod when attenuation is small.

In this particular circumstance, it is possible to specify a formalismthat is based on base elements, but that is better adapted and much moredirect.

The ZPHI algorithm can also be applied in the S band, where attenuationis small, or indeed negligible. The advantage of so doing lies inreproducing the natural variability of rain “in real time”. Use of theparameter A is then no longer strictly necessary.

An object of the invention is thus to propose a method that is simple,reliable, and effective for evaluating a precipitation rate whenattenuation is weak or negligible.

For this purpose, the present invention provides a method of using abipolar radar to estimate a precipitation rate for rain that generatesnegligible attenuation. The method includes the steps of using thebipolar radar to measure the differential phase Φ_(DP) and the apparentreflectivity Z_(e) on at least one of horizontal polarization H andvertical polarization V over a given interval [r₀, r₁] of path radiirelative to the radar. An estimate of the value N_(o)* representative ofthe dimensional distribution of rain drops is made on the basis of thedifferential phase difference in the range r₀ to r₁ and on the basis ofan integral of a function of the apparent reflectivity Z_(e) along theinterval [r₀, r₁]. A value is deduced for the precipitation rate at apoint from N₀* and the apparent reflectivity at the point.

The invention also provides an apparatus for estimating a precipitationrate, the apparatus comprising a bipolar radar and processor means, saidradar including means for measuring differential phase and reflectivityon at least one of horizontal polarization H and vertical polarizationV, the apparatus being characterized in that the processor meansimplement the various processing steps of the method according to theabove paragraph.

Other characteristics, objects, and advantages of the invention appearon reviewing the drawings and reading the following detaileddescription.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 sets forth the steps of the rainfall estimation method inaccordance with the present invention.

FIG. 2 sets forth steps of the rainfall estimation method in conformitywith a specific embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Further scope of applicability of the present invention will becomeapparent from the detailed description given hereinafter. However, itshould be understood that the detailed description and specificexamples, while indicating preferred embodiments of the invention, aregiven by way of illustration only, since various changes andmodifications within the spirit and scope of the invention will becomeapparent to those skilled in the art from this detailed description.

As in the ZPHI method, the method described below requires a coherentpolarization diversity radar. The input data are the reflectivityprofile Z_(H) (or Z_(V)), together with a measurement of thedifferential phase between the H channel and the V channel.

The purpose here is to determine the parameter N₀* (and thus therainfall rate) when attenuation is negligible, for example for rainmeasured in the S band, for rain that is sufficiently light and measuredin the C and X bands, or indeed for ice.

As in the ZPHI method, the present method makes use of two types ofdata: reflectivity Z_(H) (or Z_(V), or more generally Z_(e)) anddifferential phase Φ_(DP).

Providing attenuation is negligible, the measured reflectivity can beused directly to estimate rainfall rate R on the basis of an estimatefor the parameter N₀* which specifically constitutes the subject matterof the present method.

The method relies on the “universal” relationship associating equivalentreflectivity Z_(e) (mm⁶m⁻³) and differential phase rate K_(DP) (° km⁻¹):

$\begin{matrix}{\frac{K_{DP}}{N_{0}^{*}} = {a\left\lbrack \frac{Z_{e}}{N_{0}^{*}} \right\rbrack}^{b}} & (1)\end{matrix}$

Where a and b are coefficients specified by the diffusion model, anddepend on the type of precipitation (rain or ice crystal type) and arealso functions of temperature to a small extent. The type ofprecipitation can be determined by a classification method of the typedescribed by Straka, Zrnié, and Ryzhkov (2000).

More generally, the diffusion model defines the relationship:

$\begin{matrix}{\frac{K_{DP}}{N_{O}^{*}} = {F\left\lbrack \frac{Z_{e}}{N_{0}^{*}} \right\rbrack}} & (2)\end{matrix}$

By integrating (1) or (2) between the two bounds r₁ and r₂ of theintegration segment (r₁<r₂) the following is obtained:Φ_(DP)(r ₂)−Φ_(DP)(r ₁)=[N ₀*]^(1−b)∫_(r1) ^(r2) Z _(e) ^(b) ds  (3)

I.e.:

$\begin{matrix}{N_{0}^{*} = \left\lbrack \frac{{\Phi_{DP}\left( r_{2} \right)} - {\Phi_{DP}\left( r_{1} \right)}}{a{\int_{r1}^{r2}{Z_{e}^{b}\ {\mathbb{d}s}}}} \right\rbrack^{\frac{1}{1 - b}}} & (4)\end{matrix}$

All that is then required in order to obtain the estimate for R is tofeed this estimate for N₀* into the “universal” relationship associatingR with Z_(e):R=c└N ₀*┘^(1−d) Z _(e) ^(d)  (5)

In the general case where the relationship K_(DP)−Z_(e) is written inthe form (2), (3) becomes:

$\begin{matrix}{{{\Phi_{DP}\left( r_{2} \right)} - {\Phi_{DP}\left( r_{1} \right)}} = {N_{0}^{*}{\int_{r1}^{r2}{{F\left( \frac{Z_{e}}{N_{0}^{*}} \right)}\ {\mathbb{d}s}}}}} & (6)\end{matrix}$

An analytic solution is not then available for N₀*, but a numericalsolution can be found by an iterative numerical method using solution(4) as the first guess for N₀*.

For ice, which hardly attenuates the radar wave at all regardless of thefrequency used (X, C, and S bands), there are no fixed limits on rangeof application.

For rain, application of the method is constrained by the requirementfor attenuation to be negligible between the points r₁ and r₂ (r₂>r₁).More specifically, application conditions leading to an error of 3decibels (dB) on N₀* are as follows (for T=10° C., and for a gamma typerelationship having a form parameter equal to 2 governing droplet sizedistribution):

for X band: [Φ_(DP)(r₂)−Φ_(DP)(r₁)]=≦4°

for C band: [Φ_(DP)(r₂)−Φ_(DP)(r₁)]=≦10°

for S band: [Φ_(DP)(r₂)−Φ_(DP)(r₁)]=≦64°

The main fields of application of the invention include the same fieldsof application as for the ZPHI algorithm, i.e., estimating rain incatchment areas for flood warning and for water resource management.This application is valid for all types of rain using S band, or to rainthat is sufficiently light in C band and X band. The present inventionis also applicable to estimating precipitation in the form of ice.

The invention also presents numerous other applications in meteorology.

The invention being thus described, it will be apparent that the samemay be varied in many ways. Such variations are not to be regarded as adeparture from the spirit and scope of the invention, and all suchmodifications as would be recognized by one skilled in the art areintended to be included within the scope of the following claims.

1. A method of using a bipolar radar to estimate a precipitation ratefor rain that generates negligible attenuation, the method comprisingthe following steps: using said bipolar radar to measure thedifferential phase Φ_(DP) and the apparent reflectivity z_(e) on atleast one of horizontal polarization H and vertical polarization V overa given interval [r₀, r₁] of path radii relative to said radar; makingan estimate of the value N₀* representative of the dimensionaldistribution of rain drops on the basis of the differential phasedifference in the range r₀ to r₁ and on the basis of an integral of afunction of the apparent reflectivity Z_(e) along the interval [r₀, r₁];and deducing a value for the precipitation rate at a point from N₀* andthe apparent reflectivity at said point.
 2. The method according toclaim 1, wherein N₀* is deduced directly from the differential phasedifference between r₀ and r₁ and from the integral of the apparentreflectivity Z_(e) raised to a selected exponent.
 3. The methodaccording to claim 1, wherein the selected exponent is an exponent bsatisfying:$\frac{K_{DP}}{N_{O}^{*}} = {a\left\lbrack \frac{Z_{e}}{N_{0}^{*}} \right\rbrack}^{b}$where K_(DP) is the rate of variation in the differential phase alongthe radius, a and b being specified by the type of precipitation underconsideration and by temperature.
 4. The method according to claim 3,wherein the type of precipitation is a corresponding type selected fromrain type and ice crystal type.
 5. The method according to claim 1,wherein the apparent reflectivity function which is integrated dependson N₀*, and further comprising the step of calculating said function ina plurality of iterations using a value for N₀* as determined at apreceding iteration.
 6. The method according to claim 5, wherein N₀* iscalculated from the following relationship:${{\Phi_{DP}\left( r_{2} \right)} - {\Phi_{DP}\left( r_{1} \right)}} = {N_{0}^{*}{\int_{r1}^{r2}{{F\left( \frac{Z_{e}}{N_{0}^{*}} \right)}\ {\mathbb{d}s}}}}$where Φ_(DP) is the differential phase and where F is a functionsatisfying the following relationship:$\frac{K_{DP}}{N_{0}^{*}} = {F\left( \frac{Z_{e}}{N_{0}^{*}} \right)}$where K_(DP) is the rate of variation in differential phase along theradius.
 7. The method according to claim 5 wherein, for the firstiteration, the value used for N₀* is given by:$N_{O}^{*} = \left\lbrack \frac{{\Phi_{DP}\left( r_{2} \right)} - {\Phi_{DP}\left( r_{1} \right)}}{a{\int_{r1}^{r2}{Z_{e}^{b}\ {\mathbb{d}s}}}} \right\rbrack^{\frac{1}{1 - b}}$8. The method according to claim 1 wherein the rainfall rate R isdetermined from N₀* and from the apparent reflectivity Z_(e) by therelationship:R=c└N ₀*┘^(1−d) Z _(e) ^(d)
 9. An apparatus for estimating aprecipitation rate, comprising a bipolar radar and a processor, saidradar configured to measure differential phase and reflectivity on atleast one of horizontal polarization H and vertical polarization V, saidprocessor configured to use said bipolar radar to measure thedifferential phase Φ_(DP) and the apparent reflectivity Z_(e) on atleast one of horizontal polarization H and vertical polarization V overa given interval [r₀, r₁] of path radii relative to said radar; make anestimate of the value N₀* representative of the dimensional distributionof rain drops on the basis of the differential phase difference in therange r₀ to r₁ and on the basis of an integral of a function of theapparent reflectivity Z_(e) along the interval [r₀, r₁]; and deduce avalue for the precipitation rate at a point from N₀* and the apparentreflectivity at said point.